On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation II: Arbitrary Initial and Final Jerks

Finding smooth and fast motion functions within the kinematic limits of a robot or automated system is an important task for reducing vibration and increasing efficiency. Much research is concerned with point-to-point motion as needed in pick-and-place operations but prescribing general boundary conditions is also interesting for setting the state at intermediate waypoints in multipoint tasks or for reacting to unforeseen events having an arbitrary state. This paper addresses the following trajectory problem: jerk-continuous, fast online trajectory generation under kinematic restrictions with arbitrary initial/final velocity and jerk, while initial and final accelerations are constrained to zero. Fast means that at any time at least one restriction is reached. This extends previous work to additionally prescribing initial and final jerks and can hence be seen as an important intermediate step towards the full solution where the accelerations can also be arbitrarily chosen. We further develop the method of going systematically through the velocity–acceleration plane applied in previous research by introducing new concepts and techniques regarding how points in this plane can be connected and additional rounds can be inserted. The algorithms we develop find an admissible solution for any given distance within the timeframe suitable for online trajectory generation although a faster isolated solution might be missed. We tested the algorithm in a huge number of random configurations and show that the motion times are shorter than those the only other available algorithm provides.